Try this:

#attachmentView {
  height: 200px !important;
  min-height: 200px !important;
  overflow: auto !important; }

Help/Troubleshooting Info, Profile Folder, Open Folder, close TB, create a new folder named chrome, create a new document in chrome with a text editor, name it userChrome.css, Save as type: All files *.*, copy in the above code, change the numbers as desired. Double-click toolkit.legacyUserProfileCustomizations.stylesheets to true in Settings/General/Config. editor, restart TB.

Online css generator

https://support.mozilla.org/en-US/questions/1157661

Thank you very much: it worked!

Only a small problem remained. When I try to modify the height with the mouse I will get either 200px or 0px. Not possible to get a size in between. I changed "min-height: 100px !important;" but nothing changed (except the smaller size, but still not changeable) Any solution?

The height can be changed as shown in the attached pictures. Omit the min-height line in the code. Right-click the pane to enable 'Initially Show Attachment Pane'.

Thank you, but didn't work. If I delete min-high I get again a 1 mm high pane and no way to change it. More surprisingly when I add again min-height and delete height nothing changed! (i.e. either fixed 100px or 0px) Also the overflow can be deleted without change.

You will see a collapsed pane unless you click the > icon to expand it, or enable 'Initially Show Attachment Pane'.

Surely I know this. The strange behaviour is only regarding the fact that once the height is set to e.g. 100px I am not allowed to move this limit with tho mouse to e.g. 50px. But if for some reason this is not possible, I can live with this situation. Thank you very much for your help.

That's right, the pane can either be whatever is set in the css or collapsed to the minimum height; adjusting with the mouse is not possible, unlike with the Message Pane.

OK, I didn't know it. Learned something new. Thank you again for your help.